Tube and fitting assemblies have been devised in many different structures and methods of assembly. The usual case of a tube telescoped over a part of a fitting is where jaws of some kind have generally radially compressed the tube into sealing contact with that part of the telescoped tubing and fitting. In such case the tube is compressed radially inwardly to make the seal. This is difficult to actually make a good seal because the tube, even though malleable and has been deformed past its elastic limit, tends to have a certain amount of elasticity and springs back radially outwardly after the jaw pressure has been removed. Thus, in many cases the fluid seal between the tube and the fitting is destroyed or at least lowered as to the fluid pressure it will withstand.